• Percent body fat, although an accurate health indicator, is difficult and costly to measure
• Aim: create a model to accurately estimate a male’s percentage body fat from easily made body measurements
• Final model characteristics:
  • Backwards stepwise selection
  • BIC
  • No intercept

Percent Body Fat =

0.05795 * Age - 11.27374 * Height + 0.76046 * Abdomen - 1.84242 * Wrist

• Obesity has become an increasingly important global health problem
• Percent body fat (PBF) is an accurate indicator of weight category (e.g., obese)
• PBF is difficult, timely and expensive to measure

Aim: create a model that can predict a male’s PBF from more easily accessible measurements

1. Converted variables to metric units
2. Removed density variable - measured to directly calculate body fat percentage
3. Removed two observations with <1% body fat
4. BMI for each male was calculated and added

• Forward vs Backward
• Intercept
• BMI
• AIC vs BIC

• with BMI vs without BMI

Our final model is backward BIC model with no intercept.

##          Age       Height      Abdomen        Wrist 
##   0.05794883 -11.27373938   0.76045631  -1.84242340

## 
## Call:
## lm(formula = Pct.BF ~ Age + Height + Abdomen + Wrist - 1, data = df3)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -10.3745  -3.0720  -0.4906   3.3440   9.5735 
## 
## Coefficients:
##          Estimate Std. Error t value Pr(>|t|)    
## Age       0.05795    0.02283   2.538 0.011776 *  
## Height  -11.27374    3.23823  -3.481 0.000591 ***
## Abdomen   0.76046    0.03341  22.762  < 2e-16 ***
## Wrist    -1.84242    0.39360  -4.681 4.74e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.241 on 244 degrees of freedom
## Multiple R-squared:  0.9593, Adjusted R-squared:  0.9586 
## F-statistic:  1436 on 4 and 244 DF,  p-value: < 2.2e-16

• Predictors and outcome assumed to have a linear relationship
• Horizontal line should show no distinct patterns, however it shows some distinct patterns

• Looking further through visualizing each predictor against Body Fat shows points fairly equal above and below the line

• We are assuming data was collected in an independent manner, or errors are independent
• Data collected from Brigham Young University, fairly trusted source
• Stated 250 different men of varying ages, hopefully indicating they are all independent of each other

• Residual error assumed to be normally distributed
• Points on QQ plot are fairly close to the line up until the ends, which may be of concern
• However due to large number of observations its possible Central Limit Theorem solves this assumption

• Residuals assumed to have constant variance
• Points seem equally spread above and below the line
• Line possibly not horizontal enough, however it doesn’t seem of too much concern

Body_Fat_Percentage = 0.05795 * Age - 11.27374 * Height + 0.76046 * Abdomen - 1.84242 * Wrist

• Number of variables: 4

• P-Value:

• Adjusted R-squared value: 0.9586

The consideration of physical factors alone is limiting.

• Older people

• Shorter people

• People who work out regularly

Future study to overcome limitations:

• Diet structure

• Daily exercise time